Question

Three men are pulling on ropes attached to a tree the first man exerts a force of 6.0 N north, the second a force of 35 N east, and the third 40 N to south. What is the magnitude of the resultant force on the tree?

Answer 1

`48.8"N"` on a bearing of `134.2^@`

Explanation:

First we can find the resultant force of the men pulling in the north and south directions:

`F=40-6=34"N"` due south (180)

Now we can find the resultant of this force and the man pulling east.

Using Pythagoras:

`R^2=34^2+35^2=2381`

`:.R=sqrt(2381)=44.8"N"`

The angle `theta` from the vertical is given by:

`tantheta=35/34=1.0294`

`:.theta=45.8^@`

Taking N as zero degrees this is on a bearing of `134.2^@`